Muonic Vacuum Modes and the Temporal Geometry of Cosmic Expansion

We introduce a phenomenological framework in which discrete second‑order recurrence relations, leptonic energy scales, and Planck‑derived spectral mantissas collectively generate an emergent vacuum dynamics with Hubble‑like behavior. The vacuum is modeled as a multiscale operator supporting orbital‑like modes—electronic, muonic, redshift‑like, and X17‑like—that mix through a Temporal Orbital Mode (TOM) structure analogous to Molecular Orbital Theory. The characteristic energies 7.68 eV, 8.31 eV, and 10.17 eV arise as dimensionless spectral invariants of the recurrence system and define a nearly orthogonal basis for an effective vacuum state. Fourier analysis of the recurrence sequences reveals persistent correlation floors rather than oscillatory resonances, suggesting that vacuum fluctuations behave as correlated low‑entropy modes rather than random noise. In this picture, the muonic scale acts as a high‑velocity tunneling channel that shapes the early‑time expansion, while the redshift‑like 5.82 eV mode and the X17‑like geometric residue govern the late‑time relaxation toward a near‑zero‑point attractor. Quantum tunneling appears only as a secondary correction, whereas the dominant behavior is the emergence of a macroscopic Hubble‑like attractor driven by the interplay between spectral modes. This work is not proposed as a complete cosmological model, but as a computational and geometric bridge between discrete dynamical systems, leptonic scales, thermodynamic residues, and vacuum orbital structure.